Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.19399 | 0.689348 | 0.344674 | − | 0.938722i | \(-0.387989\pi\) | ||||
0.344674 | + | 0.938722i | \(0.387989\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.76720 | −0.790318 | −0.395159 | − | 0.918613i | \(-0.629310\pi\) | ||||
−0.395159 | + | 0.918613i | \(0.629310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.20476 | 1.58925 | 0.794624 | − | 0.607102i | \(-0.207668\pi\) | ||||
0.794624 | + | 0.607102i | \(0.207668\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.57440 | −0.524799 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.20169 | 1.86988 | 0.934940 | − | 0.354805i | \(-0.115453\pi\) | ||||
0.934940 | + | 0.354805i | \(0.115453\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.78297 | 1.88126 | 0.940629 | − | 0.339437i | \(-0.110236\pi\) | ||||
0.940629 | + | 0.339437i | \(0.110236\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.11002 | −0.544804 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.29929 | −1.04273 | −0.521366 | − | 0.853333i | \(-0.674577\pi\) | ||||
−0.521366 | + | 0.853333i | \(0.674577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.98396 | 0.684568 | 0.342284 | − | 0.939596i | \(-0.388799\pi\) | ||||
0.342284 | + | 0.939596i | \(0.388799\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.02042 | 1.09554 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.21325 | 0.878522 | 0.439261 | − | 0.898359i | \(-0.355240\pi\) | ||||
0.439261 | + | 0.898359i | \(0.355240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.87699 | −0.375398 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.46177 | −1.05112 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.933916 | 0.173424 | 0.0867119 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867119 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.70445 | 0.844944 | 0.422472 | − | 0.906376i | \(-0.361163\pi\) | ||||
0.422472 | + | 0.906376i | \(0.361163\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.40473 | 1.28900 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.43066 | −1.25601 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8223 | −1.94357 | −0.971784 | − | 0.235872i | \(-0.924205\pi\) | ||||
−0.971784 | + | 0.235872i | \(0.924205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.09877 | 1.29684 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.43611 | 1.16133 | 0.580663 | − | 0.814144i | \(-0.302793\pi\) | ||||
0.580663 | + | 0.814144i | \(0.302793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.15408 | 1.09099 | 0.545494 | − | 0.838115i | \(-0.316342\pi\) | ||||
0.545494 | + | 0.838115i | \(0.316342\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.78228 | 0.414758 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7119 | −1.70836 | −0.854182 | − | 0.519975i | \(-0.825941\pi\) | ||||
−0.854182 | + | 0.519975i | \(0.825941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.6800 | 1.52571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.13330 | −0.718805 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.02506 | 0.552884 | 0.276442 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276442 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.9597 | −1.47780 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.56281 | 0.471906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.10841 | −1.18581 | −0.592907 | − | 0.805271i | \(-0.702020\pi\) | ||||
−0.592907 | + | 0.805271i | \(0.702020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.77285 | 0.483064 | 0.241532 | − | 0.970393i | \(-0.422350\pi\) | ||||
0.241532 | + | 0.970393i | \(0.422350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.61996 | −0.834036 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.9869 | −1.48679 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.44242 | 1.15358 | 0.576788 | − | 0.816894i | \(-0.304306\pi\) | ||||
0.576788 | + | 0.816894i | \(0.304306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.03055 | 0.605608 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.31936 | 0.393935 | 0.196968 | − | 0.980410i | \(-0.436891\pi\) | ||||
0.196968 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.72218 | −0.786772 | −0.393386 | − | 0.919373i | \(-0.628696\pi\) | ||||
−0.393386 | + | 0.919373i | \(0.628696\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.24110 | −0.258780 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26.0766 | 2.97170 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.40584 | −0.158169 | −0.0790847 | − | 0.996868i | \(-0.525200\pi\) | ||||
−0.0790847 | + | 0.996868i | \(0.525200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79808 | −0.199786 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7836 | −1.51295 | −0.756475 | − | 0.654023i | \(-0.773080\pi\) | ||||
−0.756475 | + | 0.654023i | \(0.773080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.59773 | 0.824090 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.11508 | 0.119549 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.83991 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28.5207 | 2.98979 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.61704 | 0.582460 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.27327 | −0.541027 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.1719 | −1.64200 | −0.821001 | − | 0.570926i | \(-0.806584\pi\) | ||||
−0.821001 | + | 0.570926i | \(0.806584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.76393 | −0.981312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.58558 | −0.356778 | −0.178389 | − | 0.983960i | \(-0.557089\pi\) | ||||
−0.178389 | + | 0.983960i | \(0.557089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3350 | −1.41247 | −0.706234 | − | 0.707979i | \(-0.749607\pi\) | ||||
−0.706234 | + | 0.707979i | \(0.749607\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.87211 | −0.865829 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.35920 | 0.324746 | 0.162373 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162373 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50830 | 0.144469 | 0.0722343 | − | 0.997388i | \(-0.476987\pi\) | ||||
0.0722343 | + | 0.997388i | \(0.476987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.1156 | −1.33979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.50566 | −0.235712 | −0.117856 | − | 0.993031i | \(-0.537602\pi\) | ||||
−0.117856 | + | 0.993031i | \(0.537602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.44567 | −0.694312 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.6791 | −0.987283 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.0775 | −1.65716 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.4610 | 2.49645 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.87861 | 0.800558 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1530 | 1.08700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.20602 | 0.461959 | 0.230980 | − | 0.972959i | \(-0.425807\pi\) | ||||
0.230980 | + | 0.972959i | \(0.425807\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.54187 | 0.752070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.65693 | 0.319507 | 0.159754 | − | 0.987157i | \(-0.448930\pi\) | ||||
0.159754 | + | 0.987157i | \(0.448930\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5468 | 1.08795 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.65206 | 0.830717 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.705557 | 0.0602798 | 0.0301399 | − | 0.999546i | \(-0.490405\pi\) | ||||
0.0301399 | + | 0.999546i | \(0.490405\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8185 | 1.51135 | 0.755675 | − | 0.654947i | \(-0.227309\pi\) | ||||
0.755675 | + | 0.654947i | \(0.227309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.9839 | −1.17766 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 42.0659 | 3.51773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.65042 | −0.137060 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7517 | 1.05174 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.4822 | −1.35027 | −0.675136 | − | 0.737693i | \(-0.735915\pi\) | ||||
−0.675136 | + | 0.737693i | \(0.735915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.4506 | 1.74563 | 0.872814 | − | 0.488054i | \(-0.162293\pi\) | ||||
0.872814 | + | 0.488054i | \(0.162293\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.76880 | 0.547225 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.31372 | −0.667774 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5350 | −0.920595 | −0.460297 | − | 0.887765i | \(-0.652257\pi\) | ||||
−0.460297 | + | 0.887765i | \(0.652257\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.80586 | 0.381129 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.7157 | 1.39619 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.44387 | −0.113092 | −0.0565461 | − | 0.998400i | \(-0.518009\pi\) | ||||
−0.0565461 | + | 0.998400i | \(0.518009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.0857 | −1.01872 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.5365 | −1.66654 | −0.833271 | − | 0.552864i | \(-0.813535\pi\) | ||||
−0.833271 | + | 0.552864i | \(0.813535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.0087 | 2.53913 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.69795 | −0.359261 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.6116 | 0.882815 | 0.441407 | − | 0.897307i | \(-0.354479\pi\) | ||||
0.441407 | + | 0.897307i | \(0.354479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.89227 | −0.596600 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.8753 | −0.817438 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.67436 | 0.349378 | 0.174689 | − | 0.984624i | \(-0.444108\pi\) | ||||
0.174689 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7227 | −0.797010 | −0.398505 | − | 0.917166i | \(-0.630471\pi\) | ||||
−0.398505 | + | 0.917166i | \(0.630471\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.50473 | 0.332999 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8924 | 1.53604 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.6629 | −1.94978 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.9654 | −1.67049 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.67697 | −0.555486 | −0.277743 | − | 0.960655i | \(-0.589586\pi\) | ||||
−0.277743 | + | 0.960655i | \(0.589586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4524 | 1.40021 | 0.700106 | − | 0.714039i | \(-0.253136\pi\) | ||||
0.700106 | + | 0.714039i | \(0.253136\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.3122 | −1.02492 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.619732 | −0.0441541 | −0.0220770 | − | 0.999756i | \(-0.507028\pi\) | ||||
−0.0220770 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4611 | 0.812453 | 0.406226 | − | 0.913772i | \(-0.366844\pi\) | ||||
0.406226 | + | 0.913772i | \(0.366844\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2741 | 0.795215 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.92689 | 0.275614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.1411 | −0.917817 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.63333 | −0.461048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.5056 | 1.28006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2699 | 1.67081 | 0.835405 | − | 0.549634i | \(-0.185233\pi\) | ||||
0.835405 | + | 0.549634i | \(0.185233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.96327 | 0.271559 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.6427 | −0.862227 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.7811 | 1.34283 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.02619 | −0.542360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.1620 | −1.96165 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8007 | −0.790234 | −0.395117 | − | 0.918631i | \(-0.629296\pi\) | ||||
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.95513 | 0.197008 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.6700 | 0.840939 | 0.420470 | − | 0.907307i | \(-0.361865\pi\) | ||||
0.420470 | + | 0.907307i | \(0.361865\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3224 | 1.14469 | 0.572347 | − | 0.820012i | \(-0.306033\pi\) | ||||
0.572347 | + | 0.820012i | \(0.306033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 31.1351 | 2.04854 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.9692 | 0.718614 | 0.359307 | − | 0.933219i | \(-0.383013\pi\) | ||||
0.359307 | + | 0.933219i | \(0.383013\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.6974 | 1.35015 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.67855 | −0.109034 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.70714 | −0.239795 | −0.119898 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119898 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.2511 | 1.49773 | 0.748866 | − | 0.662721i | \(-0.230599\pi\) | ||||
0.748866 | + | 0.662721i | \(0.230599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.2384 | 0.913395 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.8737 | −1.20580 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.2401 | 1.28785 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.4575 | −1.04295 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.1293 | 1.64273 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.07159 | 0.568085 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.6859 | −0.728945 | −0.364473 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364473 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −49.7097 | −3.08881 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.47036 | −0.0910127 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.22217 | −0.198687 | −0.0993437 | − | 0.995053i | \(-0.531674\pi\) | ||||
−0.0993437 | + | 0.995053i | \(0.531674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.11310 | −0.436954 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.16676 | 0.499798 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.4922 | −1.31041 | −0.655203 | − | 0.755453i | \(-0.727417\pi\) | ||||
−0.655203 | + | 0.755453i | \(0.727417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1881 | 1.04410 | 0.522050 | − | 0.852915i | \(-0.325167\pi\) | ||||
0.522050 | + | 0.852915i | \(0.325167\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 34.0534 | 2.06100 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.6405 | −0.701949 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3703 | −0.863431 | −0.431715 | − | 0.902010i | \(-0.642091\pi\) | ||||
−0.431715 | + | 0.902010i | \(0.642091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.40667 | −0.443426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7574 | 1.05932 | 0.529659 | − | 0.848211i | \(-0.322320\pi\) | ||||
0.529659 | + | 0.848211i | \(0.322320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9012 | −1.48023 | −0.740113 | − | 0.672483i | \(-0.765228\pi\) | ||||
−0.740113 | + | 0.672483i | \(0.765228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.29621 | −0.372956 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.2670 | 1.84564 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.48394 | 0.0872903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.3090 | −1.13191 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.4442 | −1.54489 | −0.772444 | − | 0.635083i | \(-0.780966\pi\) | ||||
−0.772444 | + | 0.635083i | \(0.780966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0964 | 0.937170 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −33.8722 | −1.96546 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.5783 | 1.65273 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.0812 | 1.73385 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.28113 | −0.245944 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.66740 | −0.381774 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.58925 | −0.147776 | −0.0738881 | − | 0.997267i | \(-0.523541\pi\) | ||||
−0.0738881 | + | 0.997267i | \(0.523541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.1158 | −0.973682 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.6678 | 1.90912 | 0.954562 | − | 0.298012i | \(-0.0963234\pi\) | ||||
0.954562 | + | 0.298012i | \(0.0963234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.93749 | 0.166037 | 0.0830184 | − | 0.996548i | \(-0.473544\pi\) | ||||
0.0830184 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.6988 | 0.659154 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.49082 | −0.196064 | −0.0980320 | − | 0.995183i | \(-0.531255\pi\) | ||||
−0.0980320 | + | 0.995183i | \(0.531255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.79186 | 0.324282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.01083 | 0.223863 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.8289 | −0.713821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7316 | −0.706220 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.80088 | 0.0995891 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −49.2459 | −2.71501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8901 | −0.708502 | −0.354251 | − | 0.935150i | \(-0.615264\pi\) | ||||
−0.354251 | + | 0.935150i | \(0.615264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.6129 | 1.01998 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.6867 | −0.911691 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.10711 | −0.441622 | −0.220811 | − | 0.975317i | \(-0.570870\pi\) | ||||
−0.220811 | + | 0.975317i | \(0.570870\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.99172 | −0.162488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.1755 | 1.57994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4734 | 0.835483 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.89002 | −0.478623 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.219765 | 0.0117976 | 0.00589879 | − | 0.999983i | \(-0.498122\pi\) | ||||
0.00589879 | + | 0.999983i | \(0.498122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.61716 | −0.354208 | −0.177104 | − | 0.984192i | \(-0.556673\pi\) | ||||
−0.177104 | + | 0.984192i | \(0.556673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −37.0470 | −1.97742 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.86366 | −0.312091 | −0.156046 | − | 0.987750i | \(-0.549875\pi\) | ||||
−0.156046 | + | 0.987750i | \(0.549875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.86599 | −0.311334 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.5843 | −1.14236 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.2624 | −0.699963 | −0.349981 | − | 0.936757i | \(-0.613812\pi\) | ||||
−0.349981 | + | 0.936757i | \(0.613812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0960 | −0.531366 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.7880 | 1.72093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.8795 | 0.621800 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.78717 | 0.249888 | 0.124944 | − | 0.992164i | \(-0.460125\pi\) | ||||
0.124944 | + | 0.992164i | \(0.460125\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.7074 | −0.609463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9244 | 0.878670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2527 | −1.25576 | −0.627879 | − | 0.778311i | \(-0.716077\pi\) | ||||
−0.627879 | + | 0.778311i | \(0.716077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.5106 | 0.749322 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.33473 | 0.326255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2484 | −0.680527 | −0.340263 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340263 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.21591 | 0.318451 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.47967 | 0.279998 | 0.139999 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139999 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −46.0827 | −2.34859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.2634 | −0.572550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.2471 | −1.73640 | −0.868200 | − | 0.496215i | \(-0.834723\pi\) | ||||
−0.868200 | + | 0.496215i | \(0.834723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.1140 | −0.916063 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.36632 | 0.220252 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.48441 | 0.125004 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.08290 | 0.355481 | 0.177740 | − | 0.984077i | \(-0.443121\pi\) | ||||
0.177740 | + | 0.984077i | \(0.443121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.9807 | 0.749975 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.12305 | −0.355708 | −0.177854 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177854 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.9101 | 1.58956 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.17757 | 0.157895 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −73.3180 | −3.63424 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1924 | 0.949001 | 0.474500 | − | 0.880255i | \(-0.342629\pi\) | ||||
0.474500 | + | 0.880255i | \(0.342629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.842424 | 0.0415537 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −38.2986 | −1.88455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.3585 | 1.19571 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.2751 | 1.04185 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.74077 | 0.133896 | 0.0669478 | − | 0.997756i | \(-0.478674\pi\) | ||||
0.0669478 | + | 0.997756i | \(0.478674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0522 | −0.587390 | −0.293695 | − | 0.955899i | \(-0.594885\pi\) | ||||
−0.293695 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.4393 | 0.896548 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.06972 | 0.391439 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.8639 | 0.767709 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 50.2261 | 2.42494 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −41.0247 | −1.97609 | −0.988046 | − | 0.154157i | \(-0.950734\pi\) | ||||
−0.988046 | + | 0.154157i | \(0.950734\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.72121 | 0.467171 | 0.233586 | − | 0.972336i | \(-0.424954\pi\) | ||||
0.233586 | + | 0.972336i | \(0.424954\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.97058 | −0.0944820 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.5722 | 0.601409 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.3212 | 1.20852 | 0.604259 | − | 0.796788i | \(-0.293469\pi\) | ||||
0.604259 | + | 0.796788i | \(0.293469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.8145 | −0.800692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.1599 | −0.910314 | −0.455157 | − | 0.890411i | \(-0.650417\pi\) | ||||
−0.455157 | + | 0.890411i | \(0.650417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0875 | −0.573004 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.6795 | −0.930807 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8326 | 0.605607 | 0.302803 | − | 0.953053i | \(-0.402077\pi\) | ||||
0.302803 | + | 0.953053i | \(0.402077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.1165 | 2.17154 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.6117 | 1.20334 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −50.4020 | −2.36288 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7454 | 0.783315 | 0.391658 | − | 0.920111i | \(-0.371902\pi\) | ||||
0.391658 | + | 0.920111i | \(0.371902\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23.4817 | 1.09603 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.7302 | −1.43125 | −0.715624 | − | 0.698486i | \(-0.753858\pi\) | ||||
−0.715624 | + | 0.698486i | \(0.753858\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.1963 | 0.752706 | 0.376353 | − | 0.926476i | \(-0.377178\pi\) | ||||
0.376353 | + | 0.926476i | \(0.377178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.92646 | −0.460329 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.70856 | −0.264161 | −0.132080 | − | 0.991239i | \(-0.542166\pi\) | ||||
−0.132080 | + | 0.991239i | \(0.542166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.7031 | 1.83332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.7726 | −0.634610 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 44.3674 | 2.04002 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.60086 | −0.256985 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.33704 | −0.290153 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.0622 | −1.41927 | −0.709634 | − | 0.704570i | \(-0.751140\pi\) | ||||
−0.709634 | + | 0.704570i | \(0.751140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −80.1901 | −3.65635 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.1523 | 0.962461 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.5790 | 1.29770 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.41545 | 0.154769 | 0.0773844 | − | 0.997001i | \(-0.475343\pi\) | ||||
0.0773844 | + | 0.997001i | \(0.475343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.72395 | −0.0779599 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.92993 | 0.357873 | 0.178936 | − | 0.983861i | \(-0.442734\pi\) | ||||
0.178936 | + | 0.983861i | \(0.442734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.01518 | −0.180835 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.2549 | 0.775549 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.9571 | 0.626061 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.80951 | −0.170537 | −0.0852685 | − | 0.996358i | \(-0.527175\pi\) | ||||
−0.0852685 | + | 0.996358i | \(0.527175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.7142 | −1.14883 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.1279 | 0.674518 | 0.337259 | − | 0.941412i | \(-0.390500\pi\) | ||||
0.337259 | + | 0.941412i | \(0.390500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.33645 | 0.281968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.4119 | 1.75034 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.07898 | −0.269446 | −0.134723 | − | 0.990883i | \(-0.543014\pi\) | ||||
−0.134723 | + | 0.990883i | \(0.543014\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.2651 | −1.25038 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.2977 | −0.719562 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.3328 | 1.11630 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −72.6339 | −3.19444 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.8641 | 0.608567 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.12024 | −0.224322 | −0.112161 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112161 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.5817 | −0.725068 | −0.362534 | − | 0.931971i | \(-0.618088\pi\) | ||||
−0.362534 | + | 0.931971i | \(0.618088\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.42326 | −0.411265 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.2258 | −0.881050 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.24857 | −0.228199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.3403 | 0.622314 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 50.4390 | 2.18475 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.93639 | −0.256652 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.58111 | 0.240843 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 66.2339 | 2.85290 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.4638 | −0.922800 | −0.461400 | − | 0.887192i | \(-0.652653\pi\) | ||||
−0.461400 | + | 0.887192i | \(0.652653\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.8027 | −0.549417 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.66547 | −0.114176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.6068 | −1.73622 | −0.868110 | − | 0.496372i | \(-0.834665\pi\) | ||||
−0.868110 | + | 0.496372i | \(0.834665\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.93997 | −0.253512 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.78677 | 0.118720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.91122 | −0.251370 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.9452 | 1.05886 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.3887 | 1.71132 | 0.855662 | − | 0.517534i | \(-0.173150\pi\) | ||||
0.855662 | + | 0.517534i | \(0.173150\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.5259 | 2.05243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.8351 | −1.34408 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.6645 | −0.744468 | −0.372234 | − | 0.928139i | \(-0.621408\pi\) | ||||
−0.372234 | + | 0.928139i | \(0.621408\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.42801 | 0.186288 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.56047 | −0.317510 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.47503 | −0.355292 | −0.177646 | − | 0.984094i | \(-0.556848\pi\) | ||||
−0.177646 | + | 0.984094i | \(0.556848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.2737 | −0.932126 | −0.466063 | − | 0.884751i | \(-0.654328\pi\) | ||||
−0.466063 | + | 0.884751i | \(0.654328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.16619 | −0.382923 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.90821 | −0.329795 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.7794 | 1.28137 | 0.640683 | − | 0.767806i | \(-0.278651\pi\) | ||||
0.640683 | + | 0.767806i | \(0.278651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.2258 | 0.965233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.9568 | −2.40445 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.9622 | 1.03383 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.8722 | 0.780267 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.20381 | 0.297333 | 0.148667 | − | 0.988887i | \(-0.452502\pi\) | ||||
0.148667 | + | 0.988887i | \(0.452502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0379 | 0.578422 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.739951 | −0.0304375 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0481 | 0.659015 | 0.329508 | − | 0.944153i | \(-0.393117\pi\) | ||||
0.329508 | + | 0.944153i | \(0.393117\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31.9466 | 1.30968 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.6843 | 0.560063 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.40921 | −0.221014 | −0.110507 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110507 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6124 | 0.514472 | 0.257236 | − | 0.966349i | \(-0.417188\pi\) | ||||
0.257236 | + | 0.966349i | \(0.417188\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8661 | −0.605396 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −48.5292 | −1.97299 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.0031 | −1.09602 | −0.548012 | − | 0.836470i | \(-0.684615\pi\) | ||||
−0.548012 | + | 0.836470i | \(0.684615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.68865 | 0.189994 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −79.4418 | −3.21387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9168 | −1.16794 | −0.583970 | − | 0.811775i | \(-0.698502\pi\) | ||||
−0.583970 | + | 0.811775i | \(0.698502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.6903 | −0.632695 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5144 | 0.906397 | 0.453199 | − | 0.891410i | \(-0.350283\pi\) | ||||
0.453199 | + | 0.891410i | \(0.350283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5038 | 1.18586 | 0.592929 | − | 0.805255i | \(-0.297971\pi\) | ||||
0.592929 | + | 0.805255i | \(0.297971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.0118 | −0.923430 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.7602 | 1.15225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.0920 | −0.483679 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.0955 | 0.882407 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.8274 | 2.02662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.3742 | 1.12956 | 0.564779 | − | 0.825242i | \(-0.308961\pi\) | ||||
0.564779 | + | 0.825242i | \(0.308961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.9779 | 1.15177 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.20010 | −0.365095 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 72.4419 | 2.87025 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.22599 | −0.206737 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.7878 | −1.29504 | −0.647521 | − | 0.762048i | \(-0.724194\pi\) | ||||
−0.647521 | + | 0.762048i | \(0.724194\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.7781 | −0.937715 | −0.468857 | − | 0.883274i | \(-0.655334\pi\) | ||||
−0.468857 | + | 0.883274i | \(0.655334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.0952 | −0.594374 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.53047 | −0.178111 | −0.0890555 | − | 0.996027i | \(-0.528385\pi\) | ||||
−0.0890555 | + | 0.996027i | \(0.528385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −56.4876 | −2.21733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.6183 | 0.925674 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.54926 | −0.0997604 | −0.0498802 | − | 0.998755i | \(-0.515884\pi\) | ||||
−0.0498802 | + | 0.998755i | \(0.515884\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.46254 | −0.252513 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.5834 | 0.412898 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.4708 | −0.524748 | −0.262374 | − | 0.964966i | \(-0.584505\pi\) | ||||
−0.262374 | + | 0.964966i | \(0.584505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.6527 | 1.34783 | 0.673917 | − | 0.738807i | \(-0.264611\pi\) | ||||
0.673917 | + | 0.738807i | \(0.264611\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −34.8190 | −1.35226 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.1728 | −0.859826 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.93482 | 0.152357 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0899 | −0.544746 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.3981 | 0.903272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.08294 | −0.0417441 | −0.0208720 | − | 0.999782i | \(-0.506644\pi\) | ||||
−0.0208720 | + | 0.999782i | \(0.506644\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2517 | 0.394587 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.4129 | 1.09200 | 0.545998 | − | 0.837787i | \(-0.316151\pi\) | ||||
0.545998 | + | 0.837787i | \(0.316151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −67.9987 | −2.60955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.1278 | 0.579700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.95074 | 0.265963 | 0.132981 | − | 0.991119i | \(-0.457545\pi\) | ||||
0.132981 | + | 0.991119i | \(0.457545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.24686 | −0.0476402 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.6827 | 0.789092 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.3018 | 1.04012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.6966 | −1.81446 | −0.907232 | − | 0.420630i | \(-0.861809\pi\) | ||||
−0.907232 | + | 0.420630i | \(0.861809\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −41.0550 | −1.55955 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.4890 | −1.19445 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.9701 | −1.21095 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0970 | 0.495375 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.9673 | −1.54731 | −0.773657 | − | 0.633604i | \(-0.781575\pi\) | ||||
−0.773657 | + | 0.633604i | \(0.781575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.2772 | −1.33051 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.7124 | 0.930723 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0765 | −0.567009 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.52985 | 0.282790 | 0.141395 | − | 0.989953i | \(-0.454841\pi\) | ||||
0.141395 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.21335 | 0.0830072 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.8210 | 0.742302 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −74.3391 | −2.78012 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.42628 | −0.165302 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.52850 | −0.168885 | −0.0844423 | − | 0.996428i | \(-0.526911\pi\) | ||||
−0.0844423 | + | 0.996428i | \(0.526911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.2751 | −2.24476 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.7614 | 1.03246 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.75295 | −0.0651029 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.37432 | −0.199322 | −0.0996612 | − | 0.995021i | \(-0.531776\pi\) | ||||
−0.0996612 | + | 0.995021i | \(0.531776\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3947 | 0.829433 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.7575 | −1.13761 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.7891 | −1.13722 | −0.568610 | − | 0.822607i | \(-0.692519\pi\) | ||||
−0.568610 | + | 0.822607i | \(0.692519\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.5349 | −0.831213 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.5590 | 2.15705 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6744 | 0.613378 | 0.306689 | − | 0.951810i | \(-0.400779\pi\) | ||||
0.306689 | + | 0.951810i | \(0.400779\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.1664 | 0.887776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.53333 | −0.313058 | −0.156529 | − | 0.987673i | \(-0.550030\pi\) | ||||
−0.156529 | + | 0.987673i | \(0.550030\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.1274 | 1.06714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.7009 | 0.793995 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.1246 | 0.516102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0102 | 0.620709 | 0.310355 | − | 0.950621i | \(-0.399552\pi\) | ||||
0.310355 | + | 0.950621i | \(0.399552\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.19399 | 0.0435113 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.9076 | −1.37960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.82033 | −0.175198 | −0.0875989 | − | 0.996156i | \(-0.527919\pi\) | ||||
−0.0875989 | + | 0.996156i | \(0.527919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 31.1980 | 1.13241 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.5876 | −0.927549 | −0.463775 | − | 0.885953i | \(-0.653505\pi\) | ||||
−0.463775 | + | 0.885953i | \(0.653505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.34202 | 0.229596 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.9619 | −0.432482 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −61.7821 | −2.23082 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.8660 | 1.94246 | 0.971230 | − | 0.238145i | \(-0.0765393\pi\) | ||||
0.971230 | + | 0.238145i | \(0.0765393\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.9528 | −0.502497 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.6962 | 0.636489 | 0.318244 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318244 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.83019 | −0.317190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −59.3527 | −2.12927 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.1891 | 0.795007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.5856 | 0.736612 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.10083 | −0.182289 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.3847 | 0.727562 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.44792 | −0.194197 | −0.0970987 | − | 0.995275i | \(-0.530956\pi\) | ||||
−0.0970987 | + | 0.995275i | \(0.530956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.84722 | −0.136965 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.5357 | −0.374606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.5911 | 0.908768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.49294 | −0.301213 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3912 | 0.580607 | 0.290304 | − | 0.956935i | \(-0.406244\pi\) | ||||
0.290304 | + | 0.956935i | \(0.406244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.3531 | 1.78137 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.7687 | −0.380495 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.6889 | −1.47117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.3072 | −1.10343 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.6614 | −0.903325 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.33351 | −0.0820417 | −0.0410209 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410209 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.4035 | −0.435544 | −0.217772 | − | 0.976000i | \(-0.569879\pi\) | ||||
−0.217772 | + | 0.976000i | \(0.569879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.5223 | 0.719748 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.55161 | 0.0893788 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.3475 | 0.746855 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −44.9030 | −1.56904 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.7162 | −0.688101 | −0.344050 | − | 0.938951i | \(-0.611799\pi\) | ||||
−0.344050 | + | 0.938951i | \(0.611799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.4615 | 0.469237 | 0.234619 | − | 0.972087i | \(-0.424616\pi\) | ||||
0.234619 | + | 0.972087i | \(0.424616\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −13.8986 | −0.483887 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.9796 | 0.416571 | 0.208286 | − | 0.978068i | \(-0.433212\pi\) | ||||
0.208286 | + | 0.978068i | \(0.433212\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.40159 | −0.291799 | −0.145900 | − | 0.989299i | \(-0.546608\pi\) | ||||
−0.145900 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.1580 | −0.595204 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −45.9163 | −1.59091 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 38.0594 | 1.31710 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.6946 | −0.888135 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.7588 | −0.889291 | −0.444646 | − | 0.895707i | \(-0.646670\pi\) | ||||
−0.444646 | + | 0.895707i | \(0.646670\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1278 | −0.969924 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.2021 | 0.730239 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −58.3331 | −2.00672 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 115.467 | 3.96748 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.7317 | −1.02039 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −49.8101 | −1.70747 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.6635 | −0.467828 | −0.233914 | − | 0.972257i | \(-0.575153\pi\) | ||||
−0.233914 | + | 0.972257i | \(0.575153\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.30223 | 0.283930 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.2063 | 1.16846 | 0.584232 | − | 0.811587i | \(-0.301396\pi\) | ||||
0.584232 | + | 0.811587i | \(0.301396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3749 | −0.695183 | −0.347592 | − | 0.937646i | \(-0.613000\pi\) | ||||
−0.347592 | + | 0.937646i | \(0.613000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.3324 | 1.27228 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.86805 | 0.0635890 | 0.0317945 | − | 0.999494i | \(-0.489878\pi\) | ||||
0.0317945 | + | 0.999494i | \(0.489878\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.5201 | −0.697705 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.77180 | 0.0601734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.71859 | −0.295758 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 64.0477 | 2.17017 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.4609 | 0.861722 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.1006 | 1.72751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.6331 | 1.30455 | 0.652274 | − | 0.757984i | \(-0.273815\pi\) | ||||
0.652274 | + | 0.757984i | \(0.273815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.5740 | −1.06497 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5064 | 0.657188 | 0.328594 | − | 0.944471i | \(-0.393425\pi\) | ||||
0.328594 | + | 0.944471i | \(0.393425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.7268 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.2189 | 0.646036 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5921 | −0.489953 | −0.244977 | − | 0.969529i | \(-0.578780\pi\) | ||||
−0.244977 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.8900 | 0.734168 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1511 | −0.373576 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.9480 | −1.16949 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.26054 | −0.276120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.1221 | 1.13930 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.39356 | 0.146533 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.3049 | −0.576510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35.9165 | 1.19523 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.9492 | 0.629891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.9743 | −1.92501 | −0.962503 | − | 0.271271i | \(-0.912556\pi\) | ||||
−0.962503 | + | 0.271271i | \(0.912556\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.64513 | 0.187237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.3160 | 1.60078 | 0.800390 | − | 0.599479i | \(-0.204626\pi\) | ||||
0.800390 | + | 0.599479i | \(0.204626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −85.4818 | −2.82904 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.96078 | −0.263175 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.3765 | 0.507777 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.6800 | −1.04503 | −0.522514 | − | 0.852631i | \(-0.675006\pi\) | ||||
−0.522514 | + | 0.852631i | \(0.675006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.09153 | −0.101869 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.5151 | 0.741094 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.1902 | 0.729611 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.5690 | 0.741262 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.260768 | 0.00855554 | 0.00427777 | − | 0.999991i | \(-0.498638\pi\) | ||||
0.00427777 | + | 0.999991i | \(0.498638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.8686 | 1.04445 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 40.1988 | 1.31605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47.1188 | 1.54095 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.4191 | −0.340377 | −0.170189 | − | 0.985412i | \(-0.554438\pi\) | ||||
−0.170189 | + | 0.985412i | \(0.554438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.50732 | 0.114457 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3927 | 0.566985 | 0.283492 | − | 0.958974i | \(-0.408507\pi\) | ||||
0.283492 | + | 0.958974i | \(0.408507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.3302 | 1.02025 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 40.5845 | 1.32022 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2710 | 0.951181 | 0.475591 | − | 0.879667i | \(-0.342234\pi\) | ||||
0.475591 | + | 0.879667i | \(0.342234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.5964 | −1.48012 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.16799 | −0.135156 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.8612 | −1.38841 | −0.694205 | − | 0.719778i | \(-0.744244\pi\) | ||||
−0.694205 | + | 0.719778i | \(0.744244\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.5668 | 0.439011 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.91540 | 0.223543 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.96669 | 0.0957995 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.86817 | −0.286070 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.28871 | −0.170426 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.3763 | −1.10661 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3728 | −0.848093 | −0.424046 | − | 0.905640i | \(-0.639391\pi\) | ||||
−0.424046 | + | 0.905640i | \(0.639391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.3176 | −0.492071 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.7680 | 1.56504 | 0.782520 | − | 0.622625i | \(-0.213934\pi\) | ||||
0.782520 | + | 0.622625i | \(0.213934\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 74.9226 | 2.40191 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.2013 | −0.486831 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.0831 | 1.41034 | 0.705172 | − | 0.709037i | \(-0.250870\pi\) | ||||
0.705172 | + | 0.709037i | \(0.250870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.4190 | 1.35572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.37466 | −0.0758170 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.6649 | −1.42459 | −0.712294 | − | 0.701881i | \(-0.752344\pi\) | ||||
−0.712294 | + | 0.701881i | \(0.752344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.09519 | 0.0348958 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −58.7989 | −1.87159 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.1419 | 0.958457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.0263 | −0.794985 | −0.397493 | − | 0.917605i | \(-0.630120\pi\) | ||||
−0.397493 | + | 0.917605i | \(0.630120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.3905 | −0.488404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.2540 | −0.642096 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.8643 | 0.724118 | 0.362059 | − | 0.932155i | \(-0.382074\pi\) | ||||
0.362059 | + | 0.932155i | \(0.382074\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64.5704 | 2.04292 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4016.2.a.m.1.16 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.8 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.8 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.16 | 23 | 1.1 | even | 1 | trivial |